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Phase Three - Climate Change
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In the first phase of this project 351 Flagler college students were surveyed about climate change. For the second phase of this project we used the same sample of Flagler college students, but this time we divided them into two different groups. Those who live in a coastal region and those that do not. A bar chart is presented below that shows 228 Flagler college students answered yes to living in a coastal region, and 121 answered no to living in a coastal region.  

 

 

 

On this part of the report we will be giving attention to the opinions of the students on the U.S backing out of the Paris Climate Accord.  

 

First, we used methods of statistical inference to determine if the majority of Flagler college students agreed with the United States to back out of the Paris Climate Accord. First we will run a hypothesis test to find statistical evidence, and then we will use a confidence interval to estimate the percent of Flagler college students who believe it was smart to back out of the Paris Climate Accord.  

 

Second, we also used results to determine if there is a significant statistical difference between the students who loved in a coastal region and those that did not and their opinion on if it was a good idea for the United States to back out of the Paris Climate Accord, or not. Like the first portion of this report we used a hypothesis test to find statistical evidence to determine a difference and a confidence interval to estimate the percent of Flagler college students who live in a coastal region and those that do not, and disagreeing with the United States in backing out of the Paris Climate Accord.  

 

Hypothesis test 1 

 

In the sample of 93 students who agreed with backing out of the Paris Climate Accord, 67 said lived in a coastal region. That is the majority, which is 72.04% of the sample. These sample results will be used to test the claim that the majority of Flagler college students agree with backing out of the Paris Climate Accord. A pie chart is shown below to show the results.  

 

 

 

Hypothesize 

 

Null: 50% of Flagler college students believe that backing out of the Paris Climate Accord is a good idea 

 

Alternative: more than 50% of Flagler college students believe that backing out of the Paris Climate Accord is a good idea.  

 

Based on the alternative hypothesis, this is a right-sided test.  

 

Prepare 

 

1.Random sample – frankly, probably not (but we hope it is representative). However, to proceed, we will assume it is.  

2.Large samples – since nPo = (93)(.5) = 46.5 > 10 and n(1-Po) = 93(1 - .5) = 46.5 > 10 are both true statements, the sample is large.  

3.Independence within Sample – yes, the responses of the students were taken in such a way that they were independent of each other.  

 

Compute  

 

Result 3: One sample proportion Hypothesis test – agree  

 

 

Interpret  

 

Since the P-Value ( 

 

Confidence Interval 1 – estimating the population proportion  

 

The hypothesis test gives sufficient evidence that the majority of Flagler college students who agree with backing out of the Paris Climate Accord live in a coastal region. Therefore, a large sample - confidence interval was created to estimate the percent of the population of Flagler college students who believe that backing out of the Accord was a good idea. Since a one tailed test with a significance level of .05 was run, a 90% confidence interval will be created.  

 

Prepare  

 

1.Random sample with independent observations – again, probably not (but we hope it is representative). However, to proceed we will assume it is. The students responses were taken in such a way that they were independent of each other.  

2.Large sample – since n*phat = (93)(.7204) = 67 > 10 and n*(1-phat) = 93(1 - .7204) = 26 > 10, the sample is large  

Compute  

 

Result 4: One sample proportion confidence interval – Agree  

 

 

Interpret  

 

We are 90% confident that between 64% and 80% of all Flagler college students who agree with pulling out of the Paris Climate Accord live in a coastal region.  

 

Hypothesis test 2 – the difference between two populations  

 

A contingency table was created to compare those students who lived in a coastal region and those that did not, and how many disagreed with the United States backing out of the Paris Climate Accord. Of the 225 students who live in a coastal region, 158 disagreed with the decision, and of the 120 that don’t live in a coastal region, 94 disagreed with the decision. That is 70% of students who live in a coastal region, and 78% of students who do not live in a coastal region. With only an 8% difference between the two groups it shows that there is not a huge difference between the two populations.  

 

Result 5 – contingency table (with data) Coastal Vs. Non – coastal  

 

 

A hypothesis test will be used to determine if this difference is statistically significant for the population of students at Flagler college. This test will be run at a significance level of .05.  

 

Hypothesize  

 

Null: there is no difference in the proportion of population of students who live in a coastal region and the proportion of the population of students who don’t live in a coastal region and disagreeing with backing out of the Paris Climate Accord.  

 

Alternative: there is a difference in the proportion of the population of Flagler students who live in a coastal region and don’t live in a coastal region and disagreeing with backing out of the Paris Climate Accord.  

But we hope they are representative) 

Based on the alternate hypothesis, this is a two tailed test.  

 

Prepare  

 

1.Large samples – the pooled sample proportion is  

 

p-hat (X1 + X2) / (N1 + N2) = (94 + 158) / (120 + 225) = 252 / 345 = .7304  

 

sample 1 (don’t live in a coastal region):  

 

since n1 * p-hat = 120(.7304) = 88 > 10 and n1* (1 - p-hat) = 120(1 - .7304) = 32 > 10, sample is large. 

 

Sample 2 (live in a coastal region)  

 

Since n1* p-hat = 225(.7304) = 164 > 10 and n1*(1 – p-hat) = 225(1 - .7304) = 61 > 10, sample is large. 

 

2.Random samples – again, probably not (but we hope they are representative). However, to proceed we will assume they are  

3.Independent samples – yes, the students responses were taken in such a way that they were independent of each other.  

4.Independence between samples – yes, there is no relationship between the students who live in a coastal regions and the ones that do not.  

 

Compute  

 

Result  6: two sample proportion hypothesis test – coastal Vs. non – coastal  

 

 

 

Interpret  

 

since the P-value .1059 is greater than the significance level .05 we will fail to reject the null hypothesis. Therefore there is not enough sufficient evidence that there is a big difference between the amount of Flagler students who disagree with backing out of the Paris Climate Accord, and living in a coastal region or not.  

 

Confidence interval 2 – estimate the difference between to population proportions  

 

The hypothesis test did not give us enough sufficient evidence to support that there is a significant difference between the amount of students who disagree with backing out of the accord, and living in a coastal region or not. Therefore, a confidence interval was created to estimate the difference and show that there is not a large difference between the two populations.  

 

Prepare  

 

1.Random samples with independent observations – again, probably not (but we hope it is representative). However to proceed, we will assume it is. Also the students responses were taken in such a way that they are independent of each other.  

 

2.Large samples –  

 

Sample one (don’t live in a coastal region) – 

 

 since n1*p-hat1 = (120)(.78) = 93.6 > 10 and n1* (1 – p-hat1) = 120(1 - .78) = 26 > 10, sample is large. 

 

Sample two (live in a coastal region) –  

 

Since n1*p-hat1 = (225)(.702) = 158 > 10 and n1 * (1 – p-hat1) = 225(1-.702) = 67 > 10, sample is large.  

 

 

Big populations - – Recall, Flagler College has a population of appropriately 2500 students.  Since we are unsure what overall percentage of the students are or are not affected by the Paris Climate Accords, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Coastal Students and (0.50)(2500) = 1250 students who are Non-Coastal Students in the population. 

Population One (Non-Coastal Region): Since 10n1 = (10)(120) = 1200< 1250, population one is big.  

Population Two (Coastal Region): Since 10n2 = (10)(225) = 2250 > 1250, population two is small.  

4. Independent Samples – Yes, the student responses were taken in such a way that their responses were independent of each other.  

Compute 

 

Interpret 

This confidence interval is completely negative; this indicates that the percentage of the population of all Coastal Students who feel social media is a distraction is less than the percentage of the population of all Unsocial Students who feel social media is a distraction.  Thus, I am 95% confident that the percentage of all Unsocial Students who feel social media causes a distraction is between 17.6% and 1.4% greater than the percentage of all Social Students who feel social media is a distraction. 

 

 

Conclusion  

Through our hypothesis testing we found that the majority of Flagler college students who agree with backing out of the Paris Climate Accord live in a coastal region. We also found that during our second hypothesis test that there was no significant difference between backing out of the Paris Climate Accord, and whether or not students lived in or outside of a coastal region. All in all, from our research and we found that there is not a significant difference between the lives of those who live in a coastal region, and those that do not.  

 

 

 

 

Result 1: Bar Plot With Data - coastal region   [Info]
Right click to copy

Result 2: Pie Chart With Data - agree   [Info]
Right click to copy

Result 3: One sample proportion summary hypothesis test   [Info]

One sample proportion summary hypothesis test:


p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:
ProportionCountTotalSample Prop.Std. Err.Z-StatP-value
p67930.720430110.0518475854.2515019<0.0001

Result 4: One sample proportion summary confidence interval   [Info]

One sample proportion summary confidence interval:


p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.L. LimitU. Limit
p67930.720430110.0465371360.643883330.79697688

Result 5: Contingency table (with data) - Paris climate Accord and coastal region   [Info]

Contingency table results:


Rows: Coastal Region
Columns: Paris Climate Accord
AgreeDisagreeTotal
No2694120
Yes67158225
Total93252345

Chi-Square test:


StatisticDFValueP-value
Chi-square12.614930.1059

Result 6: Two sample proportion summary hypothesis test   [Info]

Two sample proportion summary hypothesis test:


p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 ≠ 0

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p2941201582250.0811111110.0501591671.61707450.1059

Result 7: Two sample proportion summary confidence interval - 95%   [Info]

Two sample proportion summary confidence interval:


p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions

95% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2941201582250.0811111110.048411906-0.0137744810.1759967

Data set 1. Moskow, Murray, Ott   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82768">Phase Three - Climate Change </A>

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